Method for tracking catheter splines in real time

Abstract

The invention relates to a method for tracking a catheter spline in real time. The present invention relates to a method for real-time tracking of a spline shape in a distal end assembly of a catheter. The method includes: (a) receiving first and second endpoint position data based on first and second position sensor assemblies respectively mounted near first and second ends of a flexible spline at a distal tip of the catheter; (b) performing a rough determination of the position of an external control point of a quadratic Bezier curve for approximating the shape of the flexible spline; (c) correcting the position of the control point; and (d) presenting the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position, and the second endpoint position.

Description

Technical Field

[0001] The presently disclosed subject matter generally relates to the field of real-time monitoring of the shape of deflectable splines of a distal tip assembly of a catheter. Background Art

[0002] US Provisional Patent Application No. 17 / 874,224 describes a technique for estimating the curvature of a spline in a catheter tip assembly using Bezier curves.

[0003] The technology includes: receiving endpoint position data and spline tangent data from a pair of position sensors mounted on opposite ends of a distal tip of a catheter, wherein the distal tip includes a plurality of flexible splines and a plurality of electrodes disposed on each of the flexible splines, and wherein the endpoint position data and spline tangent data are received when the distal tip is positioned within a heart chamber; calculating Bezier curve control points based on the endpoint position data and spline tangent data; determining estimated positions of the plurality of electrodes based on the Bezier curve control points; and updating an electroanatomical map of the heart chamber presented on a display based on the determined estimated positions.

[0004] A method for estimating the length of a Bézier curve is described by Raph Levien in an article titled “How long is that Bézier”, which can be found on the World Wide Web at the link “https: / / raphlinus.github.io / curves / 2018 / 12 / 28 / bezier-arclength.html”. Summary of the Invention

[0005] Calculating the length of a Bezier curve over multiple iterations using the techniques described in U.S. Patent Application No. 17 / 874,224 can be relatively computationally intensive. Such computational load can make it difficult and / or costly to render and display a spline curve for a catheter tip device in real time, particularly to display several (e.g., 8 or 10) spline curves for a catheter tip device in real time.

[0006] Several computationally inexpensive methods of calculating the shape of a quadratic Bezier curve and determining the estimated position of electrodes on the spline in a catheter tip assembly are described below.

[0007] The length of the splines in the catheter tip device is known, which is a physical property of the catheter tip device. The positions of the distal and proximal ends of the splines may also be known and can be measured in various ways.

[0008] In one non-limiting example method, to draw a quadratic Bezier curve corresponding to the spline shape of the catheter tip device, the outer control points P of the quadratic Bezier curve may be estimated. c Once the estimated positions of the quadratic Bezier curve control points that are not located on the Bezier curve and the measured positions of the distal and proximal ends of the spline are known, a quadratic Bezier curve that approximates the shape of the spline can be drawn, for example, on a display.

[0009] In this application and claims, when referring to a quadratic Bezier curve, the three control points of the quadratic Bezier curve are referred to as the two endpoints of the quadratic Bezier curve and an external control point of the quadratic Bezier curve that is not located on the Bezier curve.

[0010] The non-limiting exemplary method disclosed herein uses a known length of a spline to determine an estimated position of an external control point based on the positions of the proximal and distal ends of the spline, where the length of the quadratic Bezier curve is equal to (or achieves a predefined degree of consistency with) the known length of the spline.

[0011] A non-limiting example of estimating the initial position of the external control point of the quadratic Bezier curve may include constraining the position of the quadratic Bezier curve to a first predefined region based on known mechanics of the distal tip assembly. For example, estimating the position of the external control point of the quadratic Bezier curve may include determining that the initial position should be located (i.e., constrained) at a position on a particular line that is perpendicular to the straight line connecting the two endpoints of the quadratic Bezier curve and intersects the midpoint thereof.

[0012] Another non-limiting example of estimating the initial position of an external control point of a quadratic Bezier curve includes determining that the initial position should be located (ie, constrained) at a certain position on a particular line perpendicular to a straight line connecting two endpoint positions of the quadratic Bezier curve.

[0013] Another non-limiting example of estimating the initial position of an external control point of a quadratic Bezier curve can include determining that the initial position should be located at a certain position on a specific (predefined) path relative to the two endpoint positions of the quadratic Bezier curve. The predefined path can be determined by analyzing the mechanical properties (e.g., shape, flexibility, structural integrity, etc.) of the catheter distal end assembly in a calibration facility and / or the type of medical indication of the catheter.

[0014] Another non-limiting example of estimating the initial position of an external control point of a quadratic Bezier curve includes determining that the initial position should be located at a position within a specific region relative to the positions of the two endpoints of the quadratic Bezier curve. For example, the specific region (i.e., zone) can be determined based on known properties of the distal tip assembly of a catheter in a calibration facility (e.g., mechanical properties of the deflectable spline (e.g., shape, flexibility, structural integrity, etc.) and / or the type of medical indication for the catheter).

[0015] In some examples, an iterative process is used to determine the length of a quadratic Bezier curve defined based on the initial and endpoint positions of the quadratic Bezier curve's external control points based on integration of the defined quadratic Bezier curve, compare the length of the quadratic Bezier curve to the known length of the spline, and shift the new estimated positions of the quadratic Bezier curve's external control points until the estimated length of the quadratic Bezier curve is sufficiently close to the known length of the spline. The shifting of the quadratic Bezier curve's external control points can be constrained to within a first predefined region (i.e., the specific region described above). In some examples, a threshold is set to determine whether a difference between the estimated length of the quadratic Bezier curve and the known length of the spline is acceptable.

[0016] For example, the revision may include accurately calculating the length of the quadratic Bezier curve based on the initial position of the external control point, and when comparing the exact (i.e., more accurate / precise) length of the quadratic Bezier curve to the known length of the spline, the revised position of the quadratic Bezier curve may be identified.

[0017] As a non-limiting example, a more accurate method for calculating the length of a quadratic Bezier curve may optionally be a method such as that described in the aforementioned U.S. Patent Application No. 17 / 874,224. In the present disclosure, a method for accurately calculating the corrected length of a quadratic Bezier curve may generally be referred to as a numerical method (or numerical integration) hereinafter. The method may include, for example, methods such as the trapezoidal rule, Simpson's rule, quadrature method, composite method, and the like.

[0018] In some examples, an iterative process is used to calculate the length of a quadratic Bezier curve based on the integration of a defined Bezier curve. The length of the quadratic Bezier curve calculated based on the integration is compared to the known length of the spline, and the positions of the quadratic Bezier curve's external control points are shifted until the calculated length of the quadratic Bezier curve is sufficiently close to the known length of the spline. The shifting of the quadratic Bezier curve's external control points can be constrained to a second predefined area. The first predefined area and the second predefined area can have different shapes. In some examples, a threshold is set to determine whether the difference between the calculated length of the quadratic Bezier curve and the known length of the spline is acceptable.

[0019] In some examples, the above method may be used to calculate the shapes of multiple splines—the more splines whose shapes are calculated using the simplified method for the initial estimate, the greater the savings in computational load. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to better understand the subject matter disclosed herein and to illustrate how it may be implemented in practice, examples will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

[0021] Figure 1 An exemplary system is shown that can implement one or more features of the presently disclosed subject matter according to one or more examples;

[0022] Figure 2 A catheter tip assembly according to an example is shown;

[0023] Figure 3 is an illustration of a simplified method for estimating the length of a quadratic Bezier curve based on the length of a chord connecting a first endpoint location and a second endpoint location and the length of a control polyline formed by the first endpoint location, an external control point location, and the second endpoint location according to some examples;

[0024] Figure 4A is a simplified illustration of the exterior control points of a quadratic Bezier curve located on a line according to an example;

[0025] Figure 4B is a simplified illustration of the exterior control points of a quadratic Bezier curve located on a particular linear path according to an example;

[0026] Figure 5A is a simplified flowchart illustration of a method for real-time tracking of spline shapes in a catheter distal tip assembly according to an example; and

[0027] Figure 5B is a simplified flowchart illustration of a method for real-time tracking of spline shapes in a catheter distal tip assembly, according to an example. DETAILED DESCRIPTION

[0028] The presently disclosed subject matter generally relates to the field of computing the shape of a quadratic Bezier curve, and more particularly to a method of rapidly finding the locations of external control points for computing the shape of a quadratic Bezier curve representing the shape of a spline in a catheter tip assembly, and even more particularly, but not exclusively, to using the rapidly computed shape of a Bezier curve for visualization of a catheter tip assembly.

[0029] refer to Figure 1 , which illustrates an exemplary system in which one or more features of the presently disclosed subject matter can be implemented, according to one or more examples.

[0030] Figure 1 is a diagram of an exemplary system (e.g., medical device assembly) shown as system 100, in which one or more features of the subject matter herein can be implemented according to one or more embodiments. All or part of system 100 can be used to detect, diagnose, and / or treat cardiac conditions.

[0031] As shown, the system 100 includes a catheter 110 comprising a manipulator 114, a shaft 112 disposed through a sheath 113, and a distal tip in the shape of a basket (referred to herein as a "catheter basket" 116). The catheter basket 116 includes a plurality of electrodes 111 disposed on a plurality of bendable splines 109. A puller element 118 pulls or pushes the distal end 304 of the catheter basket 116, thereby expanding or collapsing the catheter basket 116. In some examples, the catheter basket 116 includes one or more position sensors that allow for sensing the position of the proximal and distal ends of the catheter basket 116.

[0032] exist Figure 1 Also shown are physician 115 (or medical professional, technician, clinician, etc.), heart 120, patient 125, and bed 130 (or table). Note that insets 140 and 150 show heart 120 and catheter 110 in greater detail. As shown, system 100 also includes console 160 (including one or more processors 222 and memory 162 that provide control and processing capabilities) and display 165. Note that each element and / or item of system 100 represents one or more of that element and / or item. Figure 1 The example of system 100 shown can be modified to implement the embodiments disclosed herein. The embodiments disclosed herein can similarly be applied using other system components and configurations. In addition, system 100 can include additional components, such as elements for sensing electrical activity, wired or wireless connectors, processing and display devices, and the like.

[0033] Treatment of cardiac conditions (such as arrhythmias) often requires obtaining detailed mapping of cardiac tissue, chambers, veins, arteries and / or electrical pathways. For example, a prerequisite for successfully performing catheter ablation (as described herein) is that the cause of the arrhythmia is accurately located in a chamber of the heart 120. Such localization can be accomplished via an electrophysiological study during which electrical potentials are detected and spatially resolved using a mapping catheter (e.g., catheter 110) introduced into a chamber of the heart 120. This electrophysiological study (so-called electroanatomical mapping) thus provides 3D mapping data that can be displayed on a monitor. In many cases, the mapping function and the therapeutic function (e.g., ablation) are provided by a single catheter or a group of catheters, such that the mapping catheter also operates simultaneously as a therapeutic (e.g., ablation) catheter. Mapping software 101 is coupled to catheter 110 to perform mapping operations as described in further detail herein.

[0034] The catheter 110 includes a plurality of flexible splines 109 and a plurality of electrodes 111 disposed on each of the flexible splines 109. The catheter 110 is configured to obtain biometric data such as electrical signals of an internal organ (e.g., the heart 120) and / or to ablate a tissue region thereof (e.g., a cardiac chamber of the heart 120).

[0035] In some examples, catheter 110 is a basket catheter. The basket catheter can be designed so that when deployed in a patient, its electrodes can remain in close contact against the endocardial surface. For example, the basket catheter can be inserted into a lumen such as a pulmonary vein (PV). The basket catheter can be inserted into the PV with the proximal end at a maximum distance from the distal end so that the basket catheter does not occupy its maximum volume when inserted into the PV. The basket catheter can be expanded by moving the proximal end toward the distal end while located within the PV so that those electrodes on the basket catheter are in contact with an entire circular segment of the PV. Such contact with the entire circular segment of the PV or any other lumen can enable effective imaging and / or ablation.

[0036] The catheter 110 and other items of the system 100 can be connected to a console 160. The console 160 can include any computing device that employs the mapping software 101. According to an exemplary embodiment, the console 160 includes one or more processors 222 (any computing hardware) and memory 162 (any non-transitory tangible medium), wherein the one or more processors 222 execute computer instructions with respect to the mapping software 101 and the memory 162 stores these instructions for execution by the one or more processors 222. For example, the console 160 can be configured to receive and / or store biometric data on a database in the memory 162, process the biometric data, and determine whether a given tissue region is conductive.

[0037] Display 165 may be any electronic device for visual presentation of biometric data, which is connected to console 160. According to an exemplary embodiment, during a procedure, console 160 may facilitate presenting a body part rendering to physician 115 on display 165 and storing data representing the body part rendering in memory 162. For example, a map depicting motion characteristics may be presented / constructed based on trajectory information sampled at a sufficient number of points in heart 120.

[0038] Among other things, the mapping software 101 maps the position of electrodes 111 of the catheter 110. The catheter 110 has position tracking elements on the proximal and distal ends of the catheter basket 116, but the electrodes 111 themselves may not have associated position sensors. The electrodes 111 may be disposed on flexible splines 109 that bend based on both the relative position of the proximal and distal ends of the catheter basket 116 and the deflection of the entire catheter 110 relative to the axis 112. Thus, the mapping software 101 operates to determine the shape and position of the splines 109 based on the detected position and orientation of the proximal and distal ends of the catheter basket 116 and the deflection angle of the catheter basket 116.

[0039] In some embodiments, the mapping software 101 generates a Bezier curve to represent the shape, position, and / or deflection of the spline 109 and obtains the position of the electrode 111 based on the shape, position, and / or deflection.

[0040] Now refer to Figure 2 , which shows a catheter tip assembly according to one example.

[0041] Figure 2 A catheter tip assembly of a basket 116 is shown, comprising a shaft 112 coupled to a proximal end 302 and a distal end 304 of the catheter basket 116. Splines 109 are coupled to the proximal end 302 and the distal end 304 of the catheter basket 116. Electrodes 111 are disposed on the splines 109. The proximal end 302 and the distal end 304 are movable relative to each other. A puller element 118 coupled to the distal end 304 of the catheter basket 116 can be pulled toward the proximal end 302 of the catheter basket to move the distal end 304 closer to the proximal end 302, or can be pushed from the proximal end 302 to move the distal end 304 further away from the proximal end 302.

[0042] Moving the distal end 304 relative to the proximal end 302 causes the splines 109 to deform. Additionally, the catheter basket 116 can deflect at an angle relative to the shaft 112 at the proximal end 302. In other words, the basket assembly can bend at the proximal end 302 relative to the "incoming angle" of the shaft 112.

[0043] For example, when a portion of the catheter basket 116, such as one or more splines 109, contacts an anatomical structure, the catheter basket 116 deflects at an angle relative to the shaft 112 at the proximal end 302. The shape of the splines 109, and therefore the position of the electrodes 111, is therefore dependent on the relative positions of the proximal end 302 and the distal end 304, as well as the deflection angle of the catheter 110 at the proximal end 302 relative to the shaft 112.

[0044] The proximal end 302 and the distal end 304 can each include one or more position sensors (a proximal end position sensor 307 and a distal end position sensor 305) so that the mapping software 101 can directly determine their three-dimensional ("3D") positions (e.g., in conjunction with the positioning system 223). However, some or even all of the splines 109 may not have position sensors and may change shape. To this end, the mapping software 101 estimates the position and shape of the splines 109 in order to use this information to calculate the shape of the splines and optionally display the splines 109.

[0045] In some examples, three single-axis sensors may be located at distal end 304 .

[0046] In some examples, not all splines have sensors.

[0047] In some examples, the distal end of the tip assembly is rigid and can define a plane. Based on this, it is possible to determine the endpoints of each spline.

[0048] Introduction

[0049] One way to calculate the arc length of a curve (including the length of a quadratic Bezier curve) is to sample the curve at a series of points and then add up the lengths of all line segments between consecutive points. This method is equivalent to flattening the curve into straight lines and then adding up the lengths of all the straight lines. This method is simple and robust, but it can be relatively slow or computationally expensive when high accuracy is required. For every doubling of the number of samples, the accuracy increases fourfold. In other words, the number of samples increases with time. and grows, where N is the inverse of the error tolerance.

[0050] A fast method for estimating the length of a quadratic Bezier curve may enable rapid determination of the shape of a spline in a catheter tip assembly, and based thereon, an estimated position of the electrodes on the spline based on knowledge of the electrode positions along the spline. This method also enables updating the spline shape and visualization of the device at the distal tip of the catheter in real time. This method may also update an electroanatomical map of the catheter tip assembly and cardiac chambers presented on a display.

[0051] As a non-limiting example, a method for simply and quickly estimating the initial position of an external control point of a quadratic Bezier curve may include using an analytical formula to estimate the length of the quadratic Bezier curve based on the length of a chord connecting the first endpoint position and the second endpoint position, and the length of a control polyline formed by the first endpoint position, the external control point position, and the second endpoint position. The initial position of the external control point can be determined as the position (or one of the positions) where the estimated length of the quadratic Bezier curve is equal to the known spline length. Determining the initial position of the control point may also involve constraining the position of the control point to a specific path.

[0052] The term "control polyline" may be used in this specification and claims to refer to a line formed by connecting a first line connecting the endpoints of a first Bezier curve to an external control point and a second line connecting the external control point to the endpoints of a second Bezier curve. A control polyline is also called a Bezier polygon or a control polygon. However, to avoid confusion between these connecting lines and closed polygons, the term "polyline" is used herein.

[0053] The estimate of the length of a quadratic Bezier curve presented in Raph Levien's article can approximate the actual length of a quadratic Bezier curve to within + / - 2%.

[0054] In some examples, estimating the initial position of an external control point of a quadratic Bezier curve can provide the external control point of the quadratic Bezier curve, which can serve as a starting point for more accurately identifying the external control point that matches the corresponding quadratic Bezier curve to the known length of the catheter spline. Accurately identifying the external control point (i.e., revising the position of the control point) can include calculating the length of the quadratic Bezier curve at the initial position, comparing the calculated length to the actual length of the spline, and determining whether the lengths are close enough to assume the shape of the spline using the shape of the quadratic Bezier curve or whether the position of the control point needs to be adjusted. In some examples, revising the position involves shifting or adjusting the position of the external control point to minimize the difference between the calculated length of the quadratic Bezier curve and the actual length of the catheter spline to below a specified threshold.

[0055] In some examples, estimating an initial position of an external control point of the quadratic Bezier curve can provide the external control point of the quadratic Bezier curve, which can be used as a starting point for iteratively determining a more accurate position of the external control point by comparing the calculated length to the actual length of the spline and determining whether the lengths are close enough to assume the shape of the spline using the shape of the quadratic Bezier curve. Otherwise, the estimated position of the external control point is shifted and the calculation is repeated.

[0056] In some examples, estimating the initial position of the quadratic Bezier curve may provide initial positions of control points of the quadratic Bezier curve, which may have been used to render the shape of a spline based on the quadratic Bezier curve.

[0057] Now refer to Figure 3 , which is an illustration of a simplified method for estimating the length of a quadratic Bezier curve based on the length of a chord connecting a first endpoint position and a second endpoint position and the length of a control polyline formed by the first endpoint position, an external control point position, and the second endpoint position according to some examples.

[0058] Figure 3A quadratic Bezier curve 405 extending from a first endpoint P1 401 to a second endpoint P2 402 and a quadratic Bezier curve control point Pc 403 are shown.

[0059] The quadratic Bezier curve 405 is a path traced by the function B(t), a given point P1 401, and the quadratic Bezier curve control points Pc 403 and P2 402, where:

[0060] B(t)= P c +(1-t) 2 (P1-P c )+t 2 (P2-P c ), where 0 < t < 1 Equation 1

[0061] Taking endpoints P1 401 and P2 402 as the known locations of the endpoints of the spline of the catheter tip assembly, and selecting initial external control points of the quadratic Bezier curve Pc 403 for curve 405 , the length of the quadratic Bezier curve 405 can be estimated.

[0062] L p , the control line of the quadratic Bezier curve (L 1c +L 2c ) for the length L of the quadratic Bezier curve 405 s The estimate is too high.

[0063] The straight line or chord L between P1 401 and P2 402 c The length of 410 underestimates the length of curve 405.

[0064] In some examples, the length L of curve 405 s Estimate of L est The analytical formula can be given by the following formula:

[0065] L est = (2L c +L p ) / 3 = 1.002L s Equation 2

[0066] Note that the estimated length L is calculated est The actual length L of the quadratic Bezier curve 405 s within the range of about 0.2%.

[0067] It should be noted that when the shape of the catheter tip assembly spline 109 is represented by the quadratic Bezier curve 405, the estimated length L is calculated. estThis can be considered to be within about 0.2% of the actual length of the catheter tip assembly spline 109.

[0068] Now, a method using an exemplary calculation, such as the exemplary calculation of Equation 2, is described, not for calculating the length L est , but is used to estimate the external control point P when the spline length is known c 403 location.

[0069] Endpoint location

[0070] In some examples, the locations of endpoints P1 401 and P2 402 are selected based on the known location of the end of the catheter tip assembly and the geometric relationship between the known location of the end of the catheter tip assembly and the endpoints of the spline 109 .

[0071] In some examples, the locations of endpoints P1 401 and / or P2 402 are selected based on the known locations of the spline tips, eg, obtained by imaging the catheter tip assembly within a patient.

[0072] In some examples, the position of endpoints P1 401 and / or P2 402 is determined based on position sensors placed at each end of spline 109 .

[0073] Example of roughly determining the position of an external control point by direct calculation

[0074] A non-limiting example of estimating the initial position of an external control point of a quadratic Bezier curve includes determining that the initial position should be located somewhere on a particular line that is perpendicular to the straight line connecting the two endpoint positions (i.e., chord) of the quadratic Bezier curve and intersects at their midpoints.

[0075] Other non-limiting examples of estimating the initial position of an external control point of a quadratic Bezier curve may include determining that the initial position should be somewhere on a particular path (possibly a linear path) or region relative to the positions of two endpoints of the quadratic Bezier curve.

[0076] Reference again Figure 3 Another non-limiting example of estimating the initial positions of the external control points of a quadratic Bezier curve is described below. c The initial position of the external control point 403 can be determined based on data indicating the orientation of the catheter spline near the first and second endpoints. Sensors located at or near the ends of the spline can allow estimation of the orientation of the catheter spline near the first and second endpoints. Thus, the initial position can be determined from the data obtained from P1 401, P2 402, and P cThe triangle (eg, polygon) defined by 403 is derived as follows: The positions of two points P1 401 and P2 402 are known, so the line L is defined. c 410. Line L at P1 401 1c The angle and the line L at P2 402 2c The angle can be determined based on the data collected by the sensor.

[0077] When line L c When the angles at 410 and P1 401 and P2 402 are all known, the triangle is completely defined and the external control point P can be calculated. c 403 location.

[0078] Now refer to Figure 4A , which is a simplified illustration of the exterior control points of a quadratic Bezier curve located on a line according to an example.

[0079] Figure 4A A quadratic Bezier curve 405 extending from a first endpoint P1 401 to a second endpoint P2 402 is shown, and an external control point P c 403A.

[0080] Figure 4A Also shown is a line L connecting the first endpoint P1 401 and the second endpoint P2 402. c 410 perpendicular to line 420A (see angle 422A), the midpoint between the two endpoints P1 401 and P2 402 and line L c 410 intersects.

[0081] In some examples, the external control point P c The position of 403A is constrained to a specific path, such as line 420A. c The rough determination of the position of 403 can be calculated by the following analysis: 1c 411A and L 2c 412A are equal in length, so by dividing the estimated length L est Set equal to the length L of the spline s , Equation 2 enables their lengths to be calculated as follows:

[0082] L s = (2L c +L p ) / 3 = (2L c +L 1c + L 2c ) / 3 = (2L c +2L 1c ) / 3 Equation 3

[0083] The positions of P1 401 and P2 402 are known, so the line L is defined. c 410. Line L is calculated by Equation 3 1c 411 and L 2c 412, so the external control point P can be calculated c 403 location.

[0084] X 424A means P c 403A and line L c The distance between the midpoints of 410, X 424A defines the external control point P c 403, which is an exemplary position obtained by moving the vehicle from the midpoint between the known positions P1 401 and P2 402 along the line L. c The following equation 4 enables direct estimation of the external control point P c 403 Location:

[0085]

[0086] Now refer to Figure 4B , which is a simplified illustration of the exterior control points of a quadratic Bezier curve located on a particular linear path according to an example.

[0087] Figure 4B A quadratic Bezier curve 405 extending from a first endpoint P1 401 to a second endpoint P2 402 is shown, and an external control point P c 403B.

[0088] Figure 4B Also shown is a line L connecting the first endpoint P1 401 and the second endpoint P2 402. c 410 is perpendicular (see angle 422B) to a line 420B at some known point P between two endpoints P1 401 and P2 402 Y 414 and line L c 410 intersects.

[0089] In some examples, the external control point P c The position of 403B is selected to be on line 420B. Y 414 and P c The first triangle defined by 403B and P2 402, P Y 414 and the second triangle defined by Pc 403B to calculate the external control point P c The 403 location is as follows:

[0090] P1 401 and P Y The distances between 414 are known and are now defined as Y 426B, P2 402 and P Y The distance between 414 is also known and is equal to (Lc-Y).

[0091] PC 403B and P Y The distance 414 is defined as X 424B.

[0092] Due to L s , L c (the distance between P1 401 and P2 402) and Y 426B are known, and angle 422B is a right angle, so X 424B can be calculated.

[0093] Calibration to determine the position of external control points

[0094] In some examples, the catheter tip assembly can be measured in a calibration laboratory, and the shape of the spline can be measured under various conditions and various distortions of the catheter tip assembly. In this case, external control points P for drawing the correct shape of the spline can be determined and recorded. c The position of the spline endpoint and the direction of the direction sensor (e.g., a single-axis sensor) can be used to determine the external control point P based on the recorded data. c For example, a lookup table can be used.

[0095] Example of external control point location determination

[0096] In some examples, the external control point Pc 403 may be selected (ie, constrained) to lie on a particular linear path (see Figure 4B The specific linear path is formed by connecting the end points of the quadratic Bezier curve 405 at a 90-degree angle through the line L c 410. See e.g. Figure 4A and Figure 4B Description.

[0097] In some examples, the external control point Pc 403 may be selected (ie, constrained) to lie on a particular linear path (see Figure 4A The specific linear path is perpendicular to the first line L connecting the endpoints of the quadratic Bezier curve 405. c 410 and passes through the midpoint of the line. Figure 4A Description.

[0098] In some of the examples, the external control point Pc 403 may be selected (ie, constrained) to follow a particular linear path at an angle to a line 410 between P1 401 and P2 402 that intersects the line 410 somewhere between P1 401 and P2 402 .

[0099] In some examples, the position of the external control point Pc 403 relative to the endpoints P1 401 and P2 402 may be constrained to a specific path or region based on known geometric and / or mechanical properties of the catheter spline and / or its medical indication.

[0100] In some examples, determining the position of the external control point Pc 403 relative to the endpoints P1 401 and P2 402 may involve measuring and / or analyzing the shape of a spline that is part of the catheter tip assembly measured / analyzed outside the patient's body.

[0101] Optionally use a second method to calculate length to improve accuracy

[0102] In some examples, after candidate locations for control points are identified in the coarse determination phase (e.g., after one or more iterations of using the estimation formula bring the accuracy level below a desired first threshold), more accurate and computationally more intensive methods are optionally used to further improve the accuracy.

[0103] In some examples, the length of the quadratic Bezier curve can optionally be calculated by a numerical method along the Bezier curve from one end point of the Bezier curve to the other end point of the Bezier curve. If the quadratic Bezier curve length calculated by the numerical method is not close enough to the actual spline length, the control points can be shifted (optionally within a second specific path / region) and the quadratic Bezier curve length can be calculated again and compared with the actual spline length until it is close enough.

[0104] In some examples, the length of the quadratic Bezier curve can optionally be calculated by a method such as that described in U.S. Provisional Patent Application No. 17 / 874,224 (as a non-limiting example). If the quadratic Bezier curve length calculated by the numerical method is not close enough to the actual spline length, the control points can be shifted (optionally within a second specific path / region) and the quadratic Bezier curve length can be calculated again and compared to the actual spline length until it is close enough.

[0105] Now refer to Figure 5A , which is a simplified flowchart illustration of a method for real-time tracking of spline shapes in a catheter distal tip assembly, according to an example.

[0106] In a first step 502, the method includes receiving first endpoint position data P1 based on a first position sensor assembly near a first end of a flexible spline installed at a distal end of a catheter, and receiving second endpoint position data P2 based on a second position sensor assembly near a second end of the flexible spline.

[0107] In a second step 504, the method includes receiving a flexible spline L of known length s . In a third step 506, the method includes defining a normal (i.e., a chord) of a line connecting spline end positions P1 and P2. In a fourth step 508, the method includes calculating an estimated (rough) position of an external control point P c . The rough determination can be based on a relationship between the known length of the flexible spline and an estimated length of a quadratic Bézier curve. The estimated length of the quadratic Bézier curve can be calculated based on the length of a chord connecting the first endpoint position and the second endpoint position and the length of a control polyline formed by the first endpoint position, the control point position, and the second endpoint position. The rough position of the control point can be a position on the normal of the chord (i.e., a first predefined path / region) for which the estimated length of the quadratic Bézier curve is equal to (or sufficiently close to) the known length of the spline.

[0108] In a fifth step 510, the method includes calculating the length of a quadratic Bézier curve L of the rough position of the control point P c using, for example, a more accurate method such as numerical integration. B

[0109] In a sixth step 512, the method includes comparing L B and Ls.

[0110] In a seventh step 514, if the absolute value |L s −L B |<T, where T is a threshold, then the quadratic Bézier curve L c defined by the endpoint positions P1 and P2 and the external control point P B is sufficiently close to the desired spline shape, and the method includes rendering the shape of the spline as a Bézier curve (514) based on P1, P2, and P c .

[0111] In an eighth step 516, if the absolute value |L s −L B |>T, then the method includes comparing the actual values of L s and L B .

[0112] In a ninth step 518, if L s [[ID=​(516), then the endpoint positions P1 and P2 and the external control point P c The quadratic Bezier curve L defined B The desired spline shape is not close enough, and the method includes moving the control point Pc away from the line connecting the spline endpoints along the normal (518), and returning to the quadratic Bezier curve L calculated according to the fifth step. B Length (510).

[0113] In the tenth step, if L s <L B , the method comprises moving the control point P along the normal toward the line connecting the ends of the spline c Shift (520), and return to calculate the quadratic Bezier curve L according to the fifth step B Length (510).

[0114] In some cases, endpoint position data P1 and P2 may be determined based on magnetic position sensing.

[0115] In some cases, endpoint position data P1 and P2 may be determined based on imaging of the catheter tip assembly.

[0116] In some cases, the length L of the flexible spline s May optionally be stored in and / or retrieved from memory.

[0117] In some cases, Figure 5A The method includes calculating the external control point P using Equation 4 in step 508. c , where Ls is the known length of the flexible spline and Lc is the calculated distance between the first endpoint position data P1 and the second endpoint position data P2.

[0118] In some examples, the normal line may intersect the line between the two endpoints at a midpoint between the two endpoints.

[0119] In some examples, the normal line may intersect a line between two endpoints at other locations, optionally based on known mechanics of catheter tip assemblies.

[0120] In some examples, the location where the normal intersects the line between the two endpoints may be predefined and / or stored in memory.

[0121] Now refer to Figure 5B , which is a simplified flowchart illustration of a method for real-time tracking of spline shapes in a catheter distal tip assembly, according to an example.

[0122] In a first step 532 , the method includes receiving first and second endpoint position data based on first and second position sensor assemblies mounted near first and second ends, respectively, of a flexible spline at a distal tip of a catheter.

[0123] In a second step 534, the method includes performing a rough determination of positions of external control points of a quadratic Bezier curve for approximating the shape of the flexible spline, wherein the quadratic Bezier curve is defined by first and second points corresponding to first and second endpoint positions and by the external control points, the rough determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve.

[0124] In a third step 536, the method comprises correcting the position of the control point by:

[0125] (i) calculating, by numerical integration of the quadratic Bezier curve, a modified length of the quadratic Bezier curve associated with the external control point position determined in the second step (534); and

[0126] (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve.

[0127] In a fourth step 538 , the method includes reproducing the shape of the flexible spline based on a quadratic Bezier curve defined by the first endpoint position, the modified control point positions determined in step 536 , and the second endpoint position.

[0128] In some embodiments, the estimated length of the quadratic Bezier curve in the rough determination is calculated based on the length of the chord connecting the first endpoint position and the second endpoint position and the length of the control polyline formed by the first endpoint position, the control point position, and the second endpoint position.

[0129] Example

[0130] The following is a non-exclusive list of some exemplary embodiments of the present disclosure. The present disclosure also includes embodiments that include less than all of the features of an embodiment and embodiments that utilize features from multiple embodiments, even if not listed below.

[0131] Example 1 :

[0132] A method for real-time tracking of a spline shape in a distal tip assembly of a catheter, comprising:

[0133] a) receiving (532) first and second endpoint position data based on first and second position sensor assemblies mounted near first and second ends of a flexible spline at a distal tip of the catheter,

[0134] b) performing a rough determination (534) of positions of external control points of a quadratic Bezier curve for approximating the shape of the flexible spline, wherein the quadratic Bezier curve is defined by a first point and a second point corresponding to the first and second endpoint positions and by the external control points, the rough determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve, wherein the estimated length of the quadratic Bezier curve in the rough determination is calculated based on a length of a chord connecting the first and second endpoint positions and a length of a control polyline formed by the first endpoint position, the control point positions, and the second endpoint position;

[0135] c) correcting the position of the control point (536) by:

[0136] (i) calculating, by numerical integration of the quadratic Bezier curve, a modified length of the quadratic Bezier curve associated with the position of the external control point determined by the rough determination,

[0137] (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve; and

[0138] d) rendering a shape of the flexible spline (538) based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position, and the second endpoint position.

[0139] Example 2 :

[0140] The method of embodiment 1, wherein the external control point position is constrained to a predefined path, and the coarse determination comprises determining a position of the external control point on the predefined path for which the estimated length of the quadratic Bezier curve is equal to the known length of the flexible spline.

[0141] Example 3 :

[0142] The method according to any one of embodiments 1 or 2, wherein the rough determination of the position of the external control point uses the formula L s =(2L c +L p ) / 3 to calculate, where Ls is the known length of the spline, L c is the length of the chord connecting the first end position and the second end position, and L p is the length of the control line of the Bezier curve formed by the first endpoint position, the external control point position and the second endpoint position.

[0143] Example 4 :

[0144] Embodiment 2: The method of any one of embodiments 2 or 3, wherein the predefined path is a linear path median and is perpendicular to the chord connecting the first endpoint location and the second endpoint location.

[0145] Example 5 :

[0146] The method of embodiment 1, wherein performing the coarse determination comprises:

[0147] (i) iteratively selecting candidate positions of the control points,

[0148] (ii) for each candidate position, calculating an estimated length of the quadratic Bezier curve, wherein the estimated length is based on the length of a control polyline formed by the first endpoint position, the control point position, and the second endpoint position, and the length of a chord connecting the first endpoint position and the second endpoint position,

[0149] (iii) comparing the estimated length of the quadratic Bezier curve with the known length of the conduit spline, and

[0150] (iv) identifying a candidate position for the control point, for which a difference between the known catheter spline length and the estimated length of the Bezier curve is below a first threshold.

[0151] Example 6 :

[0152] The method of embodiment 5, wherein the estimated length of the quadratic Bezier curve is calculated using the formula L est =(2L c +L p ) / 3 to calculate, where L est is the estimated length of the quadratic Bezier curve, L c is the length of the chord connecting the first end position and the second end position, and L p is the length of the control polyline formed by the first endpoint position, the control point position and the second endpoint position.

[0153] Example 7 :

[0154] The method according to any one of embodiments 1 to 6, wherein in the coarse determination, the candidate position is constrained to a first predefined area.

[0155] Example 8 :

[0156] The method according to any one of embodiments 1 to 7, wherein in the modification of the position of the external control point, the position of the external control point is constrained to a second predefined area.

[0157] Example 9 :

[0158] A system includes a console configured to:

[0159] a) receiving first and second endpoint position data based on first and second position sensor assemblies mounted near first and second ends of a flexible spline at a distal tip of the catheter,

[0160] b) performing a coarse determination of positions of external control points of a quadratic Bezier curve for approximating the shape of the flexible spline, wherein the quadratic Bezier curve is defined by a first point and a second point corresponding to the first and second endpoint positions and by the external control points, the coarse determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve, wherein the estimated length of the quadratic Bezier curve in the coarse determination is calculated based on a length of a chord connecting the first and second endpoint positions and a length of a control polyline formed by the first endpoint position, the control point positions, and the second endpoint position;

[0161] c) Correcting the position of the external control point by:

[0162] (i) calculating, by numerical integration of the quadratic Bezier curve, a modified length of the quadratic Bezier curve associated with the position of the external control point determined in step b),

[0163] (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve; and

[0164] d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position determined in step c), and the second endpoint position.

[0165] Example 10 .

[0166] A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform operations including:

[0167] a) receiving first and second endpoint position data based on first and second position sensor assemblies mounted near first and second ends of a flexible spline at a distal tip of the catheter,

[0168] b) performing a rough determination of positions of external control points of a quadratic Bezier curve for approximating the shape of the flexible spline, wherein the quadratic Bezier curve is defined by a first point and a second point corresponding to the first and second endpoint positions and by the external control points, the rough determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve,

[0169] c) Correcting the position of the external control point by:

[0170] (i) calculating, by numerical integration of the quadratic Bezier curve, a modified length of the quadratic Bezier curve associated with the position of the external control point determined in step b),

[0171] (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve; and

[0172] d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position determined in step c), and the second endpoint position.

[0173] Unless otherwise specifically stated, it will be apparent from this disclosure that throughout this specification, discussions utilizing terms such as "process," "calculate," "compare," "determine," "estimate," and the like refer to the actions and / or processes of a computer that manipulates data and / or transforms data into other data, the data being represented as physical (such as electronic) quantities and / or the data representing physical objects. The term "computer" should be broadly interpreted to encompass any kind of hardware-based electronic device with data processing capabilities.

[0174] The various illustrative logical blocks, modules, and algorithmic steps described in conjunction with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, and steps have been generally described above in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. The described functionality can be implemented in different ways for specific applications, but such specific implementation decisions should not be interpreted as causing any departure from the scope of this disclosure.

[0175] It will also be understood that the system according to the present disclosure can be implemented at least in part on a suitably programmed computer. Likewise, the present disclosure contemplates a computer program readable by a computer for performing the method of the present disclosure. The present disclosure also contemplates a non-transitory computer-readable memory tangibly embodying a program of instructions executable by a computer for performing the method of the present disclosure.

Claims

1. A method for real-time tracking of a spline shape in a distal tip assembly of a catheter, comprising: a) receiving first and second endpoint position data based on first and second position sensor assemblies mounted proximate first and second ends of a flexible spline at a distal tip of a catheter; b) performing a rough determination of positions of external control points of a quadratic Bezier curve for approximating the shape of a flexible spline, wherein the quadratic Bezier curve is defined by a first point and a second point corresponding to the first and second endpoint positions and by the external control points, the rough determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve, wherein the estimated length of the quadratic Bezier curve is calculated based on a length of a chord connecting the first and second endpoint positions and a length of a control polyline formed by the first endpoint position, the control point positions, and the second endpoint position; c) correcting the position of the control point by: (i) calculating, by numerical integration of the quadratic Bezier curve, a modified length of the quadratic Bezier curve associated with the external control point position determined by the coarse determination; (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve; as well as d) rendering a shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position, and the second endpoint position.

2. The method according to claim 1, wherein The external control point positions are constrained to a predefined path, and the coarse determination includes determining a position of the external control point on the predefined path for which the estimated length of the quadratic Bezier curve is equal to the known length of the flexible spline.

3. The method according to claim 1, wherein The rough determination of the position of the external control point uses the formula L s =(2L c +L p ) / 3 to calculate, where L s is the known length of the spline, L c is the length of the chord connecting the first end position and the second end position, and L p is the length of the control line of the Bezier curve formed by the first endpoint position, the external control point position and the second endpoint position.

4. The method according to claim 2, wherein: The predefined path is a median of a linear path and is perpendicular to the chord connecting the first endpoint location and the second endpoint location.

5. The method according to claim 1, wherein In the coarse determination, the position of the external control point is constrained to a first predefined area.

6. The method according to claim 1, wherein In the modifying of the position of the external control point, the position of the external control point is constrained to a second predefined area.

7. A system comprising a console, wherein the console is configured to: a) receiving first and second endpoint position data based on first and second position sensor assemblies mounted proximate first and second ends of a flexible spline at a distal tip of a catheter; b) performing a rough determination of positions of external control points of a quadratic Bezier curve for approximating the shape of the flexible spline, wherein the quadratic Bezier curve is defined by a first point and a second point corresponding to the first and second endpoint positions and by the external control points, the rough determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve; wherein the estimated length of the quadratic Bezier curve is calculated based on the length of a chord connecting the first endpoint position and the second endpoint position and the length of a control polyline formed by the first endpoint position, the control point position, and the second endpoint position; c) correcting the position of the external control point by: (i) calculating a modified length of the quadratic Bezier curve associated with the external control point position determined in step b) by numerical integration of the quadratic Bezier curve; (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve; as well as d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position determined in step c), and the second endpoint position.

8. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform operations comprising: a) receiving first and second endpoint position data based on first and second position sensor assemblies mounted proximate first and second ends of a flexible spline at a distal tip of a catheter; b) performing a rough determination of positions of external control points of a quadratic Bezier curve for approximating the shape of the flexible spline, wherein the quadratic Bezier curve is defined by a first point and a second point corresponding to the first and second endpoint positions and by the external control points, the rough determination being based on a relationship between a known length of the flexible spline and an estimated length of the quadratic Bezier curve; c) correcting the position of the external control point by: (i) calculating a modified length of the quadratic Bezier curve associated with the external control point position determined in step b) by numerical integration of the quadratic Bezier curve; (ii) adjusting the position of the external control point to minimize the difference between the known catheter spline length and the modified length of the Bezier curve; as well as d) rendering the shape of the flexible spline based on the quadratic Bezier curve defined by the first endpoint position, the modified external control point position determined in step c), and the second endpoint position.

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